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<a href="_kernel_target_alignment_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       Kernel Target Alignment - a measure of alignment of a kernel Gram matrix with labels.</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \file</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> *</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * \author      T. Glasmachers, O.Krause</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \date        2010-2012</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> *</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> *</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> *</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> *</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> *</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> *</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> */</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="preprocessor">#ifndef SHARK_OBJECTIVEFUNCTIONS_KERNELTARGETALIGNMENT_H</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#define SHARK_OBJECTIVEFUNCTIONS_KERNELTARGETALIGNMENT_H</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_objective_function_8h.html" title="AbstractObjectiveFunction.">shark/ObjectiveFunctions/AbstractObjectiveFunction.h</a>&gt;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;<a class="code" href="_dataset_8h.html">shark/Data/Dataset.h</a>&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;<a class="code" href="_data_2_statistics_8h.html">shark/Data/Statistics.h</a>&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_kernel_function_8h.html" title="abstract super class of all kernel functions">shark/Models/Kernels/AbstractKernelFunction.h</a>&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>{</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="comment"></span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">/// \defgroup kerneloptimization Kernel Optimization</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// \ingroup objfunctions</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// \ingroup kernels</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">/// \brief All kinds of objective functions to optimize kernel functions.</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">///</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment"></span><span class="comment"></span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">///  \brief Kernel Target Alignment - a measure of alignment of a kernel Gram matrix with labels.</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment">///</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">///The Kernel Target Alignment (KTA) was originally proposed in the paper:&lt;br/&gt;</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">///On Kernel-Target Alignment. N. Cristianini, J. Shawe-Taylor,</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment">///A. Elisseeff, J. Kandola. Innovations in Machine Learning, 2006.&lt;br/&gt;</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span><span class="comment">///Here we provide a version with centering of the features as proposed</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment">///in the paper:&lt;br/&gt;</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">///Two-Stage Learning Kernel Algorithms. C. Cortes, M. Mohri,</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">///A. Rostamizadeh. ICML 2010.&lt;br/&gt;</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span><span class="comment">///</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span><span class="comment">///The kernel target alignment is defined as</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span><span class="comment">///where K is the kernel Gram matrix of the data and y is the vector of</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment">///\f[ \hat A = \frac{\langle K, y y^T \rangle}{\sqrt{\langle K, K \rangle \cdot \langle y y^T, y y^T \rangle}} \f]</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">///+1/-1 valued labels. The outer product \f$y y^T\f$ corresponds to</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span><span class="comment">///an ideal Gram matrix corresponding to a kernel that maps</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="comment">///the two classes each to a single point, thus minimizing within-class</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment">///distance for fixed inter-class distance. The inner products denote the</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">///Frobenius product of matrices:</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">///http://en.wikipedia.org/wiki/Matrix_multiplication#Frobenius_product</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">///</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">///In kernel-based learning, the kernel Gram matrix \f$K\f$ is of the form</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span><span class="comment">///\f[ K_{i,j} = k(x_i, x_j) = \langle \phi(x_i), \phi(x_j) \rangle \f]</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span><span class="comment">///for a Mercer kernel function k and inputs \f$x_i, x_j\f$. In this</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span><span class="comment">///version of the KTA we use centered feature vectors. Let</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span><span class="comment">///\f[ \psi(x_i) = \phi(x_i) - \frac{1}{\ell} \sum_{j=1}^{\ell} \phi(x_j) \f]</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span><span class="comment">///denote the centered feature vectors, then the centered Gram matrix \f$K^c\f$ is given by</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span><span class="comment">///\f[ K^c_{i,j} = \langle \psi(x_i), \psi(x_j) \rangle = K_{i,j} - \frac{1}{\ell} \sum_{n=1}^\ell K_{i,n} + K_{j,n} + \frac{1}{\ell^2} \sum_{m,n=1}^\ell K_{n,m} \f]</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span><span class="comment">///The alignment measure computed by this class is the exact same formula</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span><span class="comment">///for \f$ \hat A \f$, but with \f$K^c\f$ plugged in in place of \f$K\f$.</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span><span class="comment">///</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span><span class="comment">///KTA measures the Frobenius inner product between a kernel Gram matrix</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span><span class="comment">///and this ideal matrix. The interpretation is that KTA measures how</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span><span class="comment">///well a given kernel fits a classification problem. The actual measure</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span><span class="comment">///is invariant under kernel rescaling.</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span><span class="comment">///In Shark, objective functions are minimized by convention. Therefore</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span><span class="comment">///the negative alignment \f$- \hat A\f$ is implemented. The measure is</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span><span class="comment">///extended for multi-class problems by using prototype vectors instead</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span><span class="comment">///of scalar labels.</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment">///</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment">///The following properties of KTA are important from a model selection</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment">///point of view: it is relatively fast and easy to compute, it is</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span><span class="comment">///differentiable w.r.t. the kernel function, and it is independent of</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span><span class="comment">///the actual classifier.</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="comment">/// \ingroup kerneloptimization</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span><span class="comment"></span><span class="keyword">template</span>&lt;<span class="keyword">class</span> InputType = RealVector,<span class="keyword">class</span> LabelType = <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>&gt;</div>
<div class="foldopen" id="foldopen00095" data-start="{" data-end="};">
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html">   95</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_kernel_target_alignment.html" title="Kernel Target Alignment - a measure of alignment of a kernel Gram matrix with labels.">KernelTargetAlignment</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_abstract_objective_function.html" title="Super class of all objective functions for optimization and learning.">AbstractObjectiveFunction</a>&lt; RealVector, double &gt;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>{</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_struct" href="structshark_1_1_batch.html" title="class which helps using different batch types">Batch&lt;LabelType&gt;::type</a> BatchLabelType;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment">    /// \brief Construction of the Kernel Target Alignment (KTA) from a kernel object.</span></div>
<div class="foldopen" id="foldopen00101" data-start="{" data-end="}">
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html#a87271aa945bc1f3e0801fffadccd80b6">  101</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_kernel_target_alignment.html#a87271aa945bc1f3e0801fffadccd80b6" title="Construction of the Kernel Target Alignment (KTA) from a kernel object.">KernelTargetAlignment</a>(</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputType, LabelType&gt;</a> <span class="keyword">const</span>&amp; dataset,</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>        <a class="code hl_class" href="classshark_1_1_abstract_kernel_function.html" title="Base class of all Kernel functions.">AbstractKernelFunction&lt;InputType&gt;</a>* kernel,</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>        <span class="keywordtype">bool</span> centering = <span class="keyword">true</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>    ){</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(kernel != NULL, <span class="stringliteral">&quot;[KernelTargetAlignment] kernel must not be NULL&quot;</span>);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        mep_kernel = kernel;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>        <a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#ad8888c58fd3f98e73013afb5dd4b2af1">m_features</a>|=<a class="code hl_enumvalue" href="classshark_1_1_abstract_objective_function.html#aadafeb6dfb5b649f321e7b81ac8aad1aad3475b458576c8760f28d8d81f4eda86" title="The function can be evaluated and evalDerivative returns a meaningless value (for example std::numeri...">HAS_VALUE</a>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#ad8888c58fd3f98e73013afb5dd4b2af1">m_features</a>|=<a class="code hl_enumvalue" href="classshark_1_1_abstract_objective_function.html#aadafeb6dfb5b649f321e7b81ac8aad1aab9262b57bb302f04b2561666a9068446" title="The function can propose a sensible starting point to search algorithms.">CAN_PROPOSE_STARTING_POINT</a>;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        <span class="keywordflow">if</span>(mep_kernel -&gt; hasFirstParameterDerivative())</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <a class="code hl_variable" href="classshark_1_1_abstract_objective_function.html#ad8888c58fd3f98e73013afb5dd4b2af1">m_features</a>|=<a class="code hl_enumvalue" href="classshark_1_1_abstract_objective_function.html#aadafeb6dfb5b649f321e7b81ac8aad1aa0bc7673a369df5f86ddd6ba6735f4971" title="The method evalDerivative is implemented for the first derivative and returns a sensible value.">HAS_FIRST_DERIVATIVE</a>;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        m_data = dataset;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        m_elements = dataset.<a class="code hl_function" href="group__shark__globals.html#ga5333445992cd6b14392cd80a1ab5403c" title="Returns the total number of elements.">numberOfElements</a>();</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        m_centering = centering;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        setupY(dataset.<a class="code hl_function" href="group__shark__globals.html#ga6328a5aa2570c01a5ac5f25076071663" title="Access to labels as a separate container.">labels</a>(), centering);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>    }</div>
</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment"></span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">    /// \brief From INameable: return the class name.</span></div>
<div class="foldopen" id="foldopen00124" data-start="{" data-end="}">
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html#a018b6911e9c8eac5aa28c4f89f4c5a93">  124</a></span><span class="comment"></span>    std::string <a class="code hl_function" href="classshark_1_1_kernel_target_alignment.html#a018b6911e9c8eac5aa28c4f89f4c5a93" title="From INameable: return the class name.">name</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> <span class="stringliteral">&quot;KernelTargetAlignment&quot;</span>; }</div>
</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment"></span> </div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment">    /// Return the current kernel parameters as a starting point for an optimization run.</span></div>
<div class="foldopen" id="foldopen00128" data-start="{" data-end="}">
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html#a5743503781d8d4c9ea42164e0662a281">  128</a></span><span class="comment"></span>    <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> <a class="code hl_function" href="classshark_1_1_kernel_target_alignment.html#a5743503781d8d4c9ea42164e0662a281" title="Return the current kernel parameters as a starting point for an optimization run.">proposeStartingPoint</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        <span class="keywordflow">return</span>  mep_kernel -&gt; parameterVector();</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>    }</div>
</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
<div class="foldopen" id="foldopen00133" data-start="{" data-end="}">
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html#a942e20f87c2c2b7df9fe5ec25f81ef1d">  133</a></span>    std::size_t <a class="code hl_function" href="classshark_1_1_kernel_target_alignment.html#a942e20f87c2c2b7df9fe5ec25f81ef1d" title="Accesses the number of variables.">numberOfVariables</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <span class="keywordflow">return</span> mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>();</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    }</div>
</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span><span class="comment"></span> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span><span class="comment">    /// \brief Evaluate the (centered, negative) Kernel Target Alignment (KTA).</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="comment">    /// See the class description for more details on this computation.</span></div>
<div class="foldopen" id="foldopen00140" data-start="{" data-end="}">
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html#a7def66b8de8f3008c5e5382e78509cc8">  140</a></span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_kernel_target_alignment.html#a7def66b8de8f3008c5e5382e78509cc8" title="Evaluate the (centered, negative) Kernel Target Alignment (KTA).">eval</a>(RealVector <span class="keyword">const</span>&amp; input)<span class="keyword"> const</span>{</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>        mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(input);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>        <span class="keywordflow">return</span> -evaluateKernelMatrix().error;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>    }</div>
</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span><span class="comment"></span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span><span class="comment">    /// \brief Compute the derivative of the KTA as a function of the kernel parameters.</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span><span class="comment">    /// It holds:</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span><span class="comment">    /// \f[ \langle K^c, K^c \rangle = \langle K,K \rangle  -2 \ell \langle k,k \rangle  + mk^2 \ell^2 \\</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span><span class="comment">    ///     (\langle  K^c, K^c  \rangle )&#39;  = 2 \langle K,K&#39; \rangle  -4\ell \langle k, \frac{1}{\ell} \sum_j K&#39;_ij \rangle  +2 \ell^2 mk \sum_ij 1/(\ell^2) K&#39;_ij \\</span></div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span><span class="comment">    ///   = 2 \langle K,K&#39; \rangle  -4 \langle k, \sum_j K&#39;_ij \rangle + 2 mk \sum_ij K_ij \\</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="comment">    ///   = 2 \langle K,K&#39; \rangle  -4 \langle k u^T, K&#39; \rangle + 2 mk \langle  u u^T, K&#39; \rangle \\</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span><span class="comment">    ///   = 2\langle K -2 k u^T + mk u u^T, K&#39; \rangle ) \\</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span><span class="comment">    ///     \langle Y, K^c \rangle  = \langle Y, K \rangle  - 2 n \langle y, k \rangle  + n^2 my mk \\</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span><span class="comment">    ///     (\langle  Y  , K^c  \rangle )&#39; =   \langle Y -2 y u^T + my u u^T, K&#39;  \rangle \f]</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">    /// now the derivative is computed from this values in a second sweep over the data:</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment">    /// we get:</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span><span class="comment">    /// \f[ \hat A&#39; = 1/\langle K^c,K^c \rangle ^{3/2} (\langle K^c,K^c \rangle  (\langle Y,K^c \rangle )&#39; - 0.5*\langle Y, K^c \rangle  (\langle  K^c , K^c \rangle )&#39;) \\</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span><span class="comment">    ///    = 1/\langle K^c,K^c \rangle ^{3/2} \langle  \langle K^c,K^c \rangle  (Y -2 y u^T + my u u^T)- \langle Y, K^c \rangle (K -2 k u^T+ mk u u^T),K&#39;  \rangle \\</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span><span class="comment">    ///    = 1/\langle K^c,K^c \rangle ^{3/2} \langle W,K&#39; \rangle \f]</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span><span class="comment">    ///reordering rsults in</span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span><span class="comment">    /// \f[ W= \langle K^c,K^c \rangle  Y - \langle Y, K^c \rangle K \\</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment">    ///     - 2 (\langle K^c,K^c \rangle y - \langle Y, K^c \rangle k) u^T \\</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span><span class="comment">    ///     +   (\langle K^c,K^c \rangle my - \langle Y, K^c \rangle mk) u u^T \f]</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="comment">    /// where \f$ K&#39; \f$ is the derivative of K with respct of the kernel parameters.</span></div>
<div class="foldopen" id="foldopen00166" data-start="{" data-end="}">
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"><a class="line" href="classshark_1_1_kernel_target_alignment.html#ad1f1d75eea4b7a91498a4b62972b4efb">  166</a></span><span class="comment"></span>    <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a70f0672a3c3b24c437c81243624b5307">ResultType</a> <a class="code hl_function" href="classshark_1_1_kernel_target_alignment.html#ad1f1d75eea4b7a91498a4b62972b4efb" title="Compute the derivative of the KTA as a function of the kernel parameters.">evalDerivative</a>( <span class="keyword">const</span> <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a59bfea031628e16737c66e7117eba7b5">SearchPointType</a> &amp; input, <a class="code hl_typedef" href="classshark_1_1_abstract_objective_function.html#a29804371954a360f09696adea7cfd839">FirstOrderDerivative</a> &amp; derivative )<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span>        mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#ad5e35d1a10ff36fa72ea787baa40e9ad" title="Set the parameter vector.">setParameterVector</a>(input);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span>        <span class="comment">// the drivative is calculated in two sweeps of the data. first the required statistics</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno">  169</span>        <span class="comment">// \langle K^c,K^c \rangle , mk and k are evaluated exactly as in eval</span></div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span> </div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        KernelMatrixResults results = evaluateKernelMatrix();</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span> </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>        std::size_t parameters = mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_i_parameterizable.html#aed1e8d1d4dbde387e2f6a25141ed3a20" title="Return the number of parameters.">numberOfParameters</a>();</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>        derivative.resize(parameters);</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>        derivative.clear();</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>        <a class="code hl_define" href="_open_m_p_8h.html#a8a63d79e2c3625260e6092d933f21a98" title="Set of macros to help usage of OpenMP with Shark.">SHARK_PARALLEL_FOR</a>(<span class="keywordtype">int</span> i = 0; i &lt; (int)m_data.<a class="code hl_function" href="group__shark__globals.html#gaca4b1e6083184385dba76a21b4c1d42b" title="Returns the number of batches of the set.">numberOfBatches</a>(); ++i){</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            std::size_t startX = 0;</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j != i; ++j){</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>                startX+= <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j));</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            }</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>            RealVector threadDerivative(parameters,0.0);</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>            RealVector blockDerivative;</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>            boost::shared_ptr&lt;State&gt; state = mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a9057a4a71b4d28febb171e09bbd22c07" title="Creates an internal state of the kernel.">createState</a>();</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>            RealMatrix blockK;<span class="comment">//block of the KernelMatrix</span></div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            RealMatrix blockW;<span class="comment">//block of the WeightMatrix</span></div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>            std::size_t startY = 0;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j &lt;= i; ++j){</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#abd10e3815efade90c7f9e2a7cc8bcb6c" title="Evaluates the kernel function.">eval</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i).input,m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j).input,blockK,*state);</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                mep_kernel-&gt;<a class="code hl_function" href="classshark_1_1_abstract_kernel_function.html#a48557b9834bc06ccb4e005ce441904c8" title="Computes the gradient of the parameters as a weighted sum over the gradient of all elements of the ba...">weightedParameterDerivative</a>(</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>                    m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i).input,m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j).input,</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>                    generateDerivativeWeightBlock(i,j,startX,startY,blockK,results),<span class="comment">//takes symmetry into account</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                    *state,</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>                    blockDerivative</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                );</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>                noalias(threadDerivative) += blockDerivative;</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>                startY += <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j));</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>            }</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>            <a class="code hl_define" href="_open_m_p_8h.html#a6de33df9d72bea69f903cffb391e7121">SHARK_CRITICAL_REGION</a>{</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>                noalias(derivative) += threadDerivative;</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>            }</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        }</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span>        derivative *= -1;</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        derivative /= m_elements;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">return</span> -results.error;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span> </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <a class="code hl_class" href="classshark_1_1_abstract_kernel_function.html" title="Base class of all Kernel functions.">AbstractKernelFunction&lt;InputType&gt;</a>* mep_kernel;     <span class="comment">///&lt; kernel function</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html" title="Data set for supervised learning.">LabeledData&lt;InputType,LabelType&gt;</a> m_data;      <span class="comment">///&lt; data points</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>    RealVector m_columnMeanY;                        <span class="comment">///&lt; mean label vector</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>    <span class="keywordtype">double</span> m_meanY;                                  <span class="comment">///&lt; mean label element</span></div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>    std::size_t m_numberOfClasses;                  <span class="comment">///&lt; number of classes</span></div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>    std::size_t m_elements;                          <span class="comment">///&lt; number of data points</span></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>    <span class="keywordtype">bool</span> m_centering;</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span> </div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>    <span class="keyword">struct </span>KernelMatrixResults{</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        RealVector k;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        <span class="keywordtype">double</span> KcKc;</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        <span class="keywordtype">double</span> YcKc;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>        <span class="keywordtype">double</span> error;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        <span class="keywordtype">double</span> meanK;</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>    };</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span> </div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="keywordtype">void</span> setupY(Data&lt;unsigned int&gt;<span class="keyword">const</span>&amp; labels, <span class="keywordtype">bool</span> centering){</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        <span class="comment">//preprocess Y so calculate column means and overall mean</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        <span class="comment">//the most efficient way to do this is via the class counts</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        std::vector&lt;std::size_t&gt; classCount = <a class="code hl_function" href="group__shark__globals.html#ga89490b7ed6f9285ab91cae348c7437b8" title="Returns the number of members of each class in the dataset.">classSizes</a>(labels);</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>        m_numberOfClasses = classCount.size();</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>        RealVector classMean(m_numberOfClasses);</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>        <span class="keywordtype">double</span> dm1 = m_numberOfClasses-1.0;</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        m_meanY = 0;</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != m_numberOfClasses; ++i){</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>            classMean(i) = classCount[i]-(m_elements-classCount[i])/dm1;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>            m_meanY += classCount[i] * classMean(i);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        }</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        classMean /= m_elements;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        m_meanY /= <a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(<span class="keywordtype">double</span>(m_elements));</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>        m_columnMeanY.resize(m_elements);</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != m_elements; ++i){</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>            m_columnMeanY(i) = classMean(labels.element(i));</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        }</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>        <span class="keywordflow">if</span>(!centering){</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>            m_meanY = 0;</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>            m_columnMeanY.clear();</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>        }</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>    }</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span> </div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>    <span class="keywordtype">void</span> setupY(Data&lt;RealVector&gt;<span class="keyword">const</span>&amp; labels, <span class="keywordtype">bool</span> centering){</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>        RealVector meanLabel = <a class="code hl_function" href="namespaceshark.html#a6ae694efca57e84792fcff090223437e" title="Calculates the mean vector of the input vectors.">mean</a>(labels);</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>        m_columnMeanY.resize(m_elements);</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != m_elements; ++i){</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            m_columnMeanY(i) = inner_prod(labels.element(i),meanLabel);</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>        }</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>        m_meanY=inner_prod(meanLabel,meanLabel);</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>        <span class="keywordflow">if</span>(!centering){</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            m_meanY = 0;</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            m_columnMeanY.clear();</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>        }</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>    }</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>    <span class="keywordtype">void</span> computeBlockY(UIntVector <span class="keyword">const</span>&amp; labelsi,UIntVector <span class="keyword">const</span>&amp; labelsj, RealMatrix&amp; blockY)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>        std::size_t blockSize1 = labelsi.size();</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>        std::size_t blockSize2 = labelsj.size();</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>        <span class="keywordtype">double</span> dm1 = m_numberOfClasses-1.0;</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>        <span class="keywordflow">for</span>(std::size_t k = 0; k != blockSize1; ++k){</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>            <span class="keywordflow">for</span>(std::size_t l = 0; l != blockSize2; ++l){</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>                <span class="keywordflow">if</span>( labelsi(k) ==  labelsj(l))</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>                    blockY(k,l) = 1;</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>                    blockY(k,l) = -1.0/dm1;</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>            }</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>        }</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>    }</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span> </div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>    <span class="keywordtype">void</span> computeBlockY(RealMatrix <span class="keyword">const</span>&amp; labelsi,RealMatrix <span class="keyword">const</span>&amp; labelsj, RealMatrix&amp; blockY)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>        noalias(blockY) = labelsi % trans(labelsj);</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>    }</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>    <span class="comment"></span></div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span><span class="comment">    /// Update a sub-block of the matrix \f$ \langle Y, K^x \rangle \f$.</span></div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span><span class="comment"></span>    <span class="keywordtype">double</span> updateYK(UIntVector <span class="keyword">const</span>&amp; labelsi,UIntVector <span class="keyword">const</span>&amp; labelsj, RealMatrix <span class="keyword">const</span>&amp; block)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>        std::size_t blockSize1 = labelsi.size();</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>        std::size_t blockSize2 = labelsj.size();</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        <span class="comment">//todo optimize the i=j case</span></div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        <span class="keywordtype">double</span> result = 0;</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>        <span class="keywordtype">double</span> dm1 = m_numberOfClasses-1.0;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        <span class="keywordflow">for</span>(std::size_t k = 0; k != blockSize1; ++k){</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>            <span class="keywordflow">for</span>(std::size_t l = 0; l != blockSize2; ++l){</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>                <span class="keywordflow">if</span>(labelsi(k) == labelsj(l))</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>                    result += block(k,l);</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>                    result -= block(k,l)/dm1;</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>            }</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>        }</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>        <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    }</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span><span class="comment"></span> </div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span><span class="comment">    /// Update a sub-block of the matrix \f$ \langle Y, K^x \rangle \f$.</span></div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span><span class="comment"></span>    <span class="keywordtype">double</span> updateYK(RealMatrix <span class="keyword">const</span>&amp; labelsi,RealMatrix <span class="keyword">const</span>&amp; labelsj, RealMatrix <span class="keyword">const</span>&amp; block)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span>        RealMatrix Y(labelsi.size1(), labelsj.size1());</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span>        computeBlockY(labelsi,labelsj,Y);</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno">  300</span>        <span class="keywordflow">return</span> sum(Y * block);</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span>    }</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno">  302</span><span class="comment"></span> </div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno">  303</span><span class="comment">    /// Compute a sub-block of the matrix</span></div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno">  304</span><span class="comment">    /// \f[ W = \langle K^c, K^c \rangle Y - \langle Y, K^c \rangle K -2 (\langle K^c, K^c \rangle y - \langle Y, K^c \rangle k) u^T + (\langle K^c, K^c \rangle my - \langle Y, K^c \rangle mk) u u^T \f]</span></div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span><span class="comment"></span>    RealMatrix generateDerivativeWeightBlock(</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno">  306</span>        std::size_t i, std::size_t j,</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>        std::size_t start1, std::size_t start2,</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>        RealMatrix <span class="keyword">const</span>&amp; blockK,</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>        KernelMatrixResults <span class="keyword">const</span>&amp; matrixStatistics</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    )<span class="keyword">const</span>{</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        std::size_t blockSize1 = <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i));</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        std::size_t blockSize2 = <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j));</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>        <span class="comment">//double n = m_elements;</span></div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>        <span class="keywordtype">double</span> KcKc = matrixStatistics.KcKc;</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>        <span class="keywordtype">double</span> YcKc = matrixStatistics.YcKc;</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>        <span class="keywordtype">double</span> meanK = matrixStatistics.meanK;</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>        RealMatrix blockW(blockSize1,blockSize2);</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span> </div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>        <span class="comment">//first calculate \langle Kc,Kc \rangle  Y.</span></div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        computeBlockY(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i).label,m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j).label,blockW);</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>        blockW *= KcKc;</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno">  322</span>        <span class="comment">//- \langle Y,K^c \rangle K</span></div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        blockW-=YcKc*blockK;</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>        <span class="comment">//  -2(\langle Kc,Kc \rangle y -\langle Y, K^c \rangle  k) u^T</span></div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span>        <span class="comment">// implmented as: -(\langle K^c,K^c \rangle y -2\langle Y, K^c \rangle  k) u^T -u^T(\langle K^c,K^c \rangle y -2\langle Y, K^c \rangle  k)^T</span></div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno">  326</span>        <span class="comment">//todo find out why this is correct and the calculation above is not.</span></div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>        blockW-=repeat(subrange(KcKc*m_columnMeanY - YcKc*matrixStatistics.k,start2,start2+blockSize2),blockSize1);</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>        blockW-=trans(repeat(subrange(KcKc*m_columnMeanY - YcKc*matrixStatistics.k,start1,start1+blockSize1),blockSize2));</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span>        <span class="comment">// + (\langle Kc,Kc \rangle  my-2\langle Y, Kc \rangle mk) u u^T</span></div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno">  330</span>        blockW+= KcKc*m_meanY-YcKc*meanK;</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>        blockW /= KcKc*std::sqrt(KcKc);</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>        <span class="comment">//symmetry</span></div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno">  333</span>        <span class="keywordflow">if</span>(i != j)</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>            blockW *= 2.0;</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>        <span class="keywordflow">return</span> blockW;</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno">  336</span>    }</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span><span class="comment"></span> </div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span><span class="comment">    /// \brief Evaluate the centered kernel Gram matrix.</span></div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno">  339</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span><span class="comment">    /// The computation is as follows. By means of a</span></div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span><span class="comment">    /// number of identities it holds</span></div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span><span class="comment">    /// \f[ \langle K^c, K^c \rangle = \\</span></div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span><span class="comment">    ///     \langle K^c, K^c \rangle  = \langle K,K \rangle  -2n\langle k,k \rangle  +mk^2n^2 \\</span></div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno">  344</span><span class="comment">    ///     \langle K^c, Y \rangle  = \langle K, Y \rangle  - 2 n \langle k, y \rangle  + n^2 mk my \f]</span></div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span><span class="comment">    /// where k is the row mean over K and y the row mean over y, mk, my the total means of K and Y</span></div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span><span class="comment">    /// and n the number of elements</span></div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span><span class="comment"></span>    KernelMatrixResults evaluateKernelMatrix()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno">  348</span>        <span class="comment">//it holds</span></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>        <span class="comment">// \langle K^c,K^c \rangle  = \langle K,K \rangle  -2n\langle k,k \rangle  +mk^2n^2</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>        <span class="comment">// \langle K^c,Y \rangle  = \langle K, Y \rangle  - 2 n \langle k, y \rangle  + n^2 mk my</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span>        <span class="comment">// where k is the row mean over K and y the row mean over y, mk, my the total means of K and Y</span></div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno">  352</span>        <span class="comment">// and n the number of elements</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span> </div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>        <span class="keywordtype">double</span> KK = 0; <span class="comment">//stores \langle K,K \rangle</span></div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span>        <span class="keywordtype">double</span> YK = 0; <span class="comment">//stores \langle Y,K^c \rangle</span></div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno">  356</span>        RealVector k(m_elements,0.0);<span class="comment">//stores the row/column means of K</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        <a class="code hl_define" href="_open_m_p_8h.html#a8a63d79e2c3625260e6092d933f21a98" title="Set of macros to help usage of OpenMP with Shark.">SHARK_PARALLEL_FOR</a>(<span class="keywordtype">int</span> i = 0; i &lt; (int)m_data.<a class="code hl_function" href="group__shark__globals.html#gaca4b1e6083184385dba76a21b4c1d42b" title="Returns the number of batches of the set.">numberOfBatches</a>(); ++i){</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>            std::size_t startRow = 0;</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j != i; ++j){</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno">  360</span>                startRow+= <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j));</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>            }</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>            std::size_t rowSize = <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i));</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>            <span class="keywordtype">double</span> threadKK = 0;</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno">  364</span>            <span class="keywordtype">double</span> threadYK = 0;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>            RealVector threadk(m_elements,0.0);</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>            std::size_t startColumn = 0; <span class="comment">//starting column of the current block</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span>            <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j &lt;= i; ++j){</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno">  368</span>                std::size_t columnSize = <a class="code hl_function" href="namespaceshark.html#af2ab10364feb8a631e0866dcf2f1a4ad">batchSize</a>(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j));</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>                RealMatrix blockK = (*mep_kernel)(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i).input,m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j).input);</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>                <span class="keywordflow">if</span>(i == j){</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>                    threadKK += frobenius_prod(blockK,blockK);</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>                    subrange(threadk,startColumn,startColumn+columnSize)+=sum(as_columns(blockK));<span class="comment">//update sum_rows(K)</span></div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>                    threadYK += updateYK(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i).label,m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j).label,blockK);</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span>                }</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span>                <span class="keywordflow">else</span>{<span class="comment">//use symmetry ok K</span></div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno">  376</span>                    threadKK += 2.0 * frobenius_prod(blockK,blockK);</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>                    subrange(threadk,startColumn,startColumn+columnSize)+=sum(as_columns(blockK));</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>                    subrange(threadk,startRow,startRow+rowSize)+=sum(as_rows(blockK));<span class="comment">//symmetry: block(j,i)</span></div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>                    threadYK += 2.0 * updateYK(m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(i).label,m_data.<a class="code hl_function" href="group__shark__globals.html#ga192f5eced10acf38f3ae723a3c400d98">batch</a>(j).label,blockK);</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>                }</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span>                startColumn+=columnSize;</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>            }</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>            <a class="code hl_define" href="_open_m_p_8h.html#a6de33df9d72bea69f903cffb391e7121">SHARK_CRITICAL_REGION</a>{</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>                KK += threadKK;</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>                YK +=threadYK;</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>                noalias(k) +=threadk;</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>            }</div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>        }</div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>        <span class="comment">//calculate the error</span></div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>        <span class="keywordtype">double</span> n = (double)m_elements;</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>        k /= n;<span class="comment">//means</span></div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        <span class="keywordtype">double</span> meanK = sum(k)/n;</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>        <span class="keywordflow">if</span>(!m_centering){</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>            k.clear();</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>            meanK = 0;</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>        }</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>        <span class="keywordtype">double</span> n2 = <a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(n);</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>        <span class="keywordtype">double</span> YcKc = YK-2.0*n*inner_prod(k,m_columnMeanY)+n2*m_meanY*meanK;</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>        <span class="keywordtype">double</span> KcKc = KK - 2.0*n*inner_prod(k,k)+n2*<a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(meanK);</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span> </div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>        KernelMatrixResults results;</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>        results.k=k;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>        results.YcKc = YcKc;</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>        results.KcKc = KcKc;</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>        results.meanK = meanK;</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>        results.error = YcKc/std::sqrt(KcKc)/n;</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>        <span class="keywordflow">return</span> results;</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>    }</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>};</div>
</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span> </div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span> </div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>}</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span><span class="preprocessor">#endif</span></div>
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